Introduction Tactical Model Tactical Design Validation Conclusions

Same-Day Delivery: Tactical Design

Alejandro Toriello

Stewart School of Industrial and Systems EngineeringGeorgia Institute of Technology

joint with Alex Stroh, Alan Erera

Simchi-Levi GroupCEE Department, MIT

June 12, 2020

Introduction Tactical Model Tactical Design Validation Conclusions

E-Commerce

• Pre-COVID, e-commerce was already a large and growingsector of retail and overall economy.

• About or above 10% of all US retail since 2013(Forrester Research).

• Average annual online spending to reach $2,000 per buyer in2018 (Forrester Research).

• Amazon alone accounts for almost half of US e-retail(eMarketer).

• Amazon now second to Walmart in terms of globalemployment numbers (566K vs. 2.3M); both very active ine-retail (Fortune).

• COVID has only accelerated these trends.

Introduction Tactical Model Tactical Design Validation Conclusions

E-Commerce

Introduction Tactical Model Tactical Design Validation Conclusions

Same-Day Delivery

• Intense competition, constant need for innovation – thecustomer wants it NOW.

• Same-day delivery (SDD) further erodes brick-and-mortaradvantage. But...

• Extremely costly “last mile”.

• Lower order numbers, fewer economies of scale.

• Fewer than 1/4 of customers willing to pay, and then onlysmall amount (McKinsey).

• Flat fees (e.g. Amazon Prime) may help amortize costs.

Introduction Tactical Model Tactical Design Validation Conclusions

Same-Day Delivery

• Intense competition, constant need for innovation – thecustomer wants it NOW.

• Same-day delivery (SDD) further erodes brick-and-mortaradvantage. But...

• Extremely costly “last mile”.

• Lower order numbers, fewer economies of scale.

• Fewer than 1/4 of customers willing to pay, and then onlysmall amount (McKinsey).

• Flat fees (e.g. Amazon Prime) may help amortize costs.

Introduction Tactical Model Tactical Design Validation Conclusions

Same-Day DeliveryWhat’s new?

• Traditional delivery: order acceptance, picking and packingbefore last-mile distribution.

• Same-day delivery: simultaneous order acceptance, picking,packing and last-mile distribution.

• This talk: Delivery by end of day/common order deadline.

• Food/grocery delivery: order-specific delivery times, 30minutes to two hours (Amazon Restaurants, GrubHub,Uber Eats, pizza delivery).

Introduction Tactical Model Tactical Design Validation Conclusions

Same-Day DeliveryWhat’s new?

• Traditional delivery: order acceptance, picking and packingbefore last-mile distribution.

• Same-day delivery: simultaneous order acceptance, picking,packing and last-mile distribution.

• This talk: Delivery by end of day/common order deadline.

• Food/grocery delivery: order-specific delivery times, 30minutes to two hours (Amazon Restaurants, GrubHub,Uber Eats, pizza delivery).

Introduction Tactical Model Tactical Design Validation Conclusions

Same-Day DeliveryWhat’s new?

Source: A. Erera

Introduction Tactical Model Tactical Design Validation Conclusions

Same-Day Delivery

• Operational Models

• Azi/Gendreau/Potvin (12,14), Campbell/Savelsbergh (05),

Klapp/Erera/T. (18a,b,20), Ulmer (17a,b), Ulmer/Thomas (18),

Ulmer/Thomas/Mattfeld (18), Voccia/Campbell/Thomas (17), ...

• Can be used for tactical analysis, but complex and nottransparent.

• Our Goal: Simple, “higher-level” model capturing typicalsystem behavior.

• What does the “average” SDD operating day look like?

Introduction Tactical Model Tactical Design Validation Conclusions

Same-Day Delivery

• Operational Models

• Azi/Gendreau/Potvin (12,14), Campbell/Savelsbergh (05),

Klapp/Erera/T. (18a,b,20), Ulmer (17a,b), Ulmer/Thomas (18),

Ulmer/Thomas/Mattfeld (18), Voccia/Campbell/Thomas (17), ...

• Can be used for tactical analysis, but complex and nottransparent.

• Our Goal: Simple, “higher-level” model capturing typicalsystem behavior.

• What does the “average” SDD operating day look like?

Introduction Tactical Model Tactical Design Validation Conclusions

Outline

Tactical Model

Tactical Design Examples

Computational Validation

Conclusions and Ongoing Work

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical Dispatching Model

0 N T

• Single depot with vehicle fleet serving fixed region.

• Orders appear at constant unit rate from 0 to N.

• All orders must be served, dispatches complete by T > N.

• Objective: Minimize total dispatching time.

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical Dispatching ModelDispatch time

n f (n)

• A dispatch to serve n orders takes f (n) time, where

f (0) = 0, f is increasing, concave, can “keep up”.

• Motivation: f (n) = a + bn + c√n for n > 0, where

• c√n is a BHH (59) routing time approximation,

• assuming order locations are randomly distributed.

• Continuous approximations widely used in logistics(Franceschetti/Jabali/Laporte 17), including urban logistics(Carlsson/Song 18, Figliozzi 07, van Heeswijk/Mes/Schutten 17).

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical Dispatching ModelDispatch time

n f (n)

• A dispatch to serve n orders takes f (n) time, where

f (0) = 0, f is increasing, concave, can “keep up”.

• Motivation: f (n) = a + bn + c√n for n > 0, where

• c√n is a BHH (59) routing time approximation,

• assuming order locations are randomly distributed.

• Continuous approximations widely used in logistics(Franceschetti/Jabali/Laporte 17), including urban logistics(Carlsson/Song 18, Figliozzi 07, van Heeswijk/Mes/Schutten 17).

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical Dispatching ModelDispatch time

n f (n)

• A dispatch to serve n orders takes f (n) time, where

f (0) = 0, f is increasing, concave, can “keep up”.

• Motivation: f (n) = a + bn + c√n for n > 0, where

• c√n is a BHH (59) routing time approximation,

• assuming order locations are randomly distributed.

• Continuous approximations widely used in logistics(Franceschetti/Jabali/Laporte 17), including urban logistics(Carlsson/Song 18, Figliozzi 07, van Heeswijk/Mes/Schutten 17).

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical Dispatching ModelDispatch time

• For example, for

1. unit square service region, center depot,

2. Manhattan distances,

3. roughly 30 locations sampled uniformly,

we estimate TSP length as 1.04√n.

E[TSPn] ≈ 1.04√n

� • •

••

•

••

• ••

•

• Asymptotic constant in this case estimated at ≈ 0.89(Johnson/McGeoch/Rothberg 96).

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical Dispatching ModelDispatch time

• Realistic situation:

1. 8 mile by 8 mile service region (center depot)

2. 25 mph average vehicle speed, Manhattan distances

3. an order every 6 minutes

4. 5-minute dispatch setup, 2-minute delivery per order

• We convert this to

f (n) = 5/6 + 1/3n + 3.3√n (× 6 minutes).

Introduction Tactical Model Tactical Design Validation Conclusions

Optimal StructureConcavity abhors balance

Dispatches should be as unbalanced as possible:

• This looks nice,

• but this is better,

• and so is this!

Introduction Tactical Model Tactical Design Validation Conclusions

Optimal StructureConcavity abhors balance

Dispatches should be as unbalanced as possible:

• This looks nice,

• but this is better,

• and so is this!

Introduction Tactical Model Tactical Design Validation Conclusions

Optimal StructureConcavity abhors balance

Dispatches should be as unbalanced as possible:

• This looks nice,

• but this is better,

• and so is this!

Introduction Tactical Model Tactical Design Validation Conclusions

Consequences and Intuition

1. Decreasing dispatch lengths as day progresses.

• Matches empirical observations in operational models(KET 18a,b).

2. Dispatching (and each vehicle) start inactive, then becomeactive and remain so for rest of day.

• Useful for shift scheduling.

3. A dispatch takes all currently unserved orders.

• Vehicles can be “pre-loaded”.

• Not necessarily true with geographic order discrimination.

Introduction Tactical Model Tactical Design Validation Conclusions

Consequences and Intuition

1. Decreasing dispatch lengths as day progresses.

• Matches empirical observations in operational models(KET 18a,b).

2. Dispatching (and each vehicle) start inactive, then becomeactive and remain so for rest of day.

• Useful for shift scheduling.

3. A dispatch takes all currently unserved orders.

• Vehicles can be “pre-loaded”.

• Not necessarily true with geographic order discrimination.

Introduction Tactical Model Tactical Design Validation Conclusions

Consequences and Intuition

1. Decreasing dispatch lengths as day progresses.

• Matches empirical observations in operational models(KET 18a,b).

2. Dispatching (and each vehicle) start inactive, then becomeactive and remain so for rest of day.

• Useful for shift scheduling.

3. A dispatch takes all currently unserved orders.

• Vehicles can be “pre-loaded”.

• Not necessarily true with geographic order discrimination.

Introduction Tactical Model Tactical Design Validation Conclusions

Many VehiclesOptimal policy

t1 t2 t3

T

• Each vehicle

1. takes all available orders,

2. leaves such that its dispatch ends at T .

• Compute by solving equations of the form

t1 + f (t1) = T , t2 + f (t2 − t1) = T ,

t3 + f (N − t2) = T , . . .

Introduction Tactical Model Tactical Design Validation Conclusions

Many VehiclesOptimal policy

t1

t2 t3

T

• Each vehicle

1. takes all available orders,

2. leaves such that its dispatch ends at T .

• Compute by solving equations of the form

t1 + f (t1) = T ,

t2 + f (t2 − t1) = T ,

t3 + f (N − t2) = T , . . .

Introduction Tactical Model Tactical Design Validation Conclusions

Many VehiclesOptimal policy

t1 t2

t3

T

• Each vehicle

1. takes all available orders,

2. leaves such that its dispatch ends at T .

• Compute by solving equations of the form

t1 + f (t1) = T , t2 + f (t2 − t1) = T ,

t3 + f (N − t2) = T , . . .

Introduction Tactical Model Tactical Design Validation Conclusions

Many VehiclesOptimal policy

t1 t2 t3 T

• Each vehicle

1. takes all available orders,

2. leaves such that its dispatch ends at T .

• Compute by solving equations of the form

t1 + f (t1) = T , t2 + f (t2 − t1) = T ,

t3 + f (N − t2) = T , . . .

Introduction Tactical Model Tactical Design Validation Conclusions

One VehicleOptimal policy

t1 t2

T

1. Each dispatch takes all available orders.

2. No waiting between dispatches.

3. Last dispatch returns at T .

* Minimum dispatch quantity for all dispatches except possibly last one.

• Try solving progressively higher-order equations:

t1 + f (N) = T , (one dispatch)

t1 + f (t1) + f (N − t1) = T , (two)

t1 + f (t1) + f (f (t1)) + f (N − t1 − f (t1)) = T , . . . (three)

Introduction Tactical Model Tactical Design Validation Conclusions

One VehicleOptimal policy

t1

t2

T

1. Each dispatch takes all available orders.

2. No waiting between dispatches.

3. Last dispatch returns at T .

* Minimum dispatch quantity for all dispatches except possibly last one.

• Try solving progressively higher-order equations:

t1 + f (N) = T , (one dispatch)

t1 + f (t1) + f (N − t1) = T , (two)

t1 + f (t1) + f (f (t1)) + f (N − t1 − f (t1)) = T , . . . (three)

Introduction Tactical Model Tactical Design Validation Conclusions

One VehicleOptimal policy

t1 t2 T

1. Each dispatch takes all available orders.

2. No waiting between dispatches.

3. Last dispatch returns at T .

* Minimum dispatch quantity for all dispatches except possibly last one.

• Try solving progressively higher-order equations:

t1 + f (N) = T , (one dispatch)

t1 + f (t1) + f (N − t1) = T , (two)

t1 + f (t1) + f (f (t1)) + f (N − t1 − f (t1)) = T , . . . (three)

Introduction Tactical Model Tactical Design Validation Conclusions

One VehicleOptimal policy

t1 t2 T

1. Each dispatch takes all available orders.

2. No waiting between dispatches.

3. Last dispatch returns at T .

* Minimum dispatch quantity for all dispatches except possibly last one.

• Try solving progressively higher-order equations:

t1 + f (N) = T , (one dispatch)

t1 + f (t1) + f (N − t1) = T , (two)

t1 + f (t1) + f (f (t1)) + f (N − t1 − f (t1)) = T , . . . (three)

Introduction Tactical Model Tactical Design Validation Conclusions

Finite Fleet

T

• Optimality depends on parameters; no general structure.

• Hybrid heuristic: For m vehicles,

1. first m − 1 follow many-vehicle policy,

2. last one serves remainder with one-vehicle policy.

• For f (n) = bn + c√n, heuristic has approximation guarantee

m − 1 + Dm

√Dm

m − 1 + Dm,

Dm is number of dispatches for m-th vehicle.

Introduction Tactical Model Tactical Design Validation Conclusions

Finite Fleet

T

• Optimality depends on parameters; no general structure.

• Hybrid heuristic: For m vehicles,

1. first m − 1 follow many-vehicle policy,

2. last one serves remainder with one-vehicle policy.

• For f (n) = bn + c√n, heuristic has approximation guarantee

m − 1 + Dm

√Dm

m − 1 + Dm,

Dm is number of dispatches for m-th vehicle.

Introduction Tactical Model Tactical Design Validation Conclusions

Finite Fleet

T

• Optimality depends on parameters; no general structure.

• Hybrid heuristic: For m vehicles,

1. first m − 1 follow many-vehicle policy,

2. last one serves remainder with one-vehicle policy.

• For f (n) = bn + c√n, heuristic has approximation guarantee

m − 1 + Dm

√Dm

m − 1 + Dm,

Dm is number of dispatches for m-th vehicle.

Introduction Tactical Model Tactical Design Validation Conclusions

Finite Fleet

T

• Optimality depends on parameters; no general structure.

• Hybrid heuristic: For m vehicles,

1. first m − 1 follow many-vehicle policy,

2. last one serves remainder with one-vehicle policy.

• For f (n) = bn + c√n, heuristic has approximation guarantee

m − 1 + Dm

√Dm

m − 1 + Dm,

Dm is number of dispatches for m-th vehicle.

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical DesignFleet sizing

1. 8× 8 mile region, uniformly random locations.

2. An order every 8 minutes for 10 hours, 12-hour day.

3. Manhattan norm, 25 mph, 1 minute service per order.

• Many Vehicles: Two dispatches, 64 and 11 orders.

• Single Vehicle: Two dispatches, 55 and 20 orders.

• Dispatch time increase of only 4%!

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical DesignFleet sizing

1. 8× 8 mile region, uniformly random locations.

2. An order every 8 minutes for 10 hours, 12-hour day.

3. Manhattan norm, 25 mph, 1 minute service per order.

• Many Vehicles: Two dispatches, 64 and 11 orders.

• Single Vehicle: Two dispatches, 55 and 20 orders.

• Dispatch time increase of only 4%!

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical DesignChoosing order cutoff N

• If revenue is linear in orders served,how long do we accept orders?

• Assume fleet can be as large as necessary.

• Optimal to maximally utilize dispatched vehicles:

t1 t2 t3 T

One vehicle: Can prove similar result for one, two dispatches.

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical DesignChoosing order cutoff N

• If revenue is linear in orders served,how long do we accept orders?

• Assume fleet can be as large as necessary.

• Optimal to maximally utilize dispatched vehicles:

t1

t2

T

One vehicle: Can prove similar result for one, two dispatches.

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical DesignChoosing order cutoff N

• If revenue is linear in orders served,how long do we accept orders?

• Assume fleet can be as large as necessary.

• Optimal to maximally utilize dispatched vehicles:

t1 t2 T

One vehicle: Can prove similar result for one, two dispatches.

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical DesignChoosing order cutoff N

• If revenue is linear in orders served,how long do we accept orders?

• Assume fleet can be as large as necessary.

• Optimal to maximally utilize dispatched vehicles:

t1 t2 t3 T

One vehicle: Can prove similar result for one, two dispatches.

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical DesignChoosing order cutoff N

• If revenue is linear in orders served,how long do we accept orders?

• Assume fleet can be as large as necessary.

• Optimal to maximally utilize dispatched vehicles:

t1 t2 t3 T

One vehicle: Can prove similar result for one, two dispatches.

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical Design

Other potential applications:

1. Service region partitioning.

• Small areas served by single vehicle,or large area served by many?

2. Combining SDD and overnight deliveries.

• Starting the day with orders accumulated.

3. Length of work day, size of service region, ...

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical Design

Other potential applications:

1. Service region partitioning.

• Small areas served by single vehicle,or large area served by many?

2. Combining SDD and overnight deliveries.

• Starting the day with orders accumulated.

3. Length of work day, size of service region, ...

Introduction Tactical Model Tactical Design Validation Conclusions

Tactical Design

Other potential applications:

1. Service region partitioning.

• Small areas served by single vehicle,or large area served by many?

2. Combining SDD and overnight deliveries.

• Starting the day with orders accumulated.

3. Length of work day, size of service region, ...

Introduction Tactical Model Tactical Design Validation Conclusions

Computational ValidationCase study in Northeastern Atlanta

• 22 census tracts, about 92,000 people.

• Five addresses per tract, 110 total.

• Depot in northeast border.

• Service day: 9AM - 6PM.

• Orders every six minutes.

• Location chosen proportional to tract’spopulation times median income.

• Driving times given by Google API.

• Driving time calibrated to 24√n minutes.

• 10-min setup per dispatch,1.5-min service per order.

Introduction Tactical Model Tactical Design Validation Conclusions

Computational ValidationCase study in Northeastern Atlanta

• 22 census tracts, about 92,000 people.

• Five addresses per tract, 110 total.

• Depot in northeast border.

• Service day: 9AM - 6PM.

• Orders every six minutes.

• Location chosen proportional to tract’spopulation times median income.

• Driving times given by Google API.

• Driving time calibrated to 24√n minutes.

• 10-min setup per dispatch,1.5-min service per order.

Introduction Tactical Model Tactical Design Validation Conclusions

Computational ValidationCase study in Northeastern Atlanta

• 22 census tracts, about 92,000 people.

• Five addresses per tract, 110 total.

• Depot in northeast border.

• Service day: 9AM - 6PM.

• Orders every six minutes.

• Location chosen proportional to tract’spopulation times median income.

• Driving times given by Google API.

• Driving time calibrated to 24√n minutes.

• 10-min setup per dispatch,1.5-min service per order.

Introduction Tactical Model Tactical Design Validation Conclusions

Computational ValidationBenchmarks

• Two-vehicle fleet:

• Order cutoff at 3:40 (N = 66.7) for full utilization.

• Model predicts 389 minutes of dispatch time.

• Operational benchmark:

• Poisson arrivals (6-min. rate).

• Compute TSP for all accumulated orders, dispatch when

setup + service time + TSP = remaining time.

• Hindsight-optimal benchmark:

• Dispatch with full knowledge of each order’s time and location.

• Lower bound for any operational policy.

Introduction Tactical Model Tactical Design Validation Conclusions

Computational ValidationBenchmarks

• Two-vehicle fleet:

• Order cutoff at 3:40 (N = 66.7) for full utilization.

• Model predicts 389 minutes of dispatch time.

• Operational benchmark:

• Poisson arrivals (6-min. rate).

• Compute TSP for all accumulated orders, dispatch when

setup + service time + TSP = remaining time.

• Hindsight-optimal benchmark:

• Dispatch with full knowledge of each order’s time and location.

• Lower bound for any operational policy.

Introduction Tactical Model Tactical Design Validation Conclusions

Computational ValidationBenchmarks

• Two-vehicle fleet:

• Order cutoff at 3:40 (N = 66.7) for full utilization.

• Model predicts 389 minutes of dispatch time.

• Operational benchmark:

• Poisson arrivals (6-min. rate).

• Compute TSP for all accumulated orders, dispatch when

setup + service time + TSP = remaining time.

• Hindsight-optimal benchmark:

• Dispatch with full knowledge of each order’s time and location.

• Lower bound for any operational policy.

Introduction Tactical Model Tactical Design Validation Conclusions

Computational ValidationResults

Tactical Operational

HSO

Dispatch 1 48.40 units 48.20 units

43.90 units

249.58 min. 249.69 min.

228.07 min.

Dispatch 2 18.26 units 18.45 units

22.75 units

139.95 min. 139.16 min.

144.88 min.

Total 66.66 units 66.65 units

66.65 units

389.53 min. 388.85 min.

372.95 min.

• Benchmark metrics computed over 300 simulations.

• Tactical predictions vs. operational observations within 1%.

• Similar results for one-vehicle case, different cutoff.

Introduction Tactical Model Tactical Design Validation Conclusions

Computational ValidationResults

Tactical Operational HSO

Dispatch 1 48.40 units 48.20 units 43.90 units249.58 min. 249.69 min. 228.07 min.

Dispatch 2 18.26 units 18.45 units 22.75 units139.95 min. 139.16 min. 144.88 min.

Total 66.66 units 66.65 units 66.65 units389.53 min. 388.85 min. 372.95 min.

• Benchmark metrics computed over 300 simulations.

• Tactical predictions vs. operational observations within 1%.

• Similar results for one-vehicle case, different cutoff.

Introduction Tactical Model Tactical Design Validation Conclusions

Conclusions

• Expect unbalanced dispatches in SDD.

• Decreasing dispatch lengths.

• Divide day into inactive/active parts.

• Use policy structure for tactical design.

• Fleet sizing, cutoff time, partitioning, ...

• Accurate operational predictions (within 1% or less).

Introduction Tactical Model Tactical Design Validation Conclusions

Ongoing Work

• Choosing service region(s) and cutoff time(s).

• Should we serve different customers differently?

• In-town versus suburban, near versus far...

• Region partitioning and fleet sizing in tandem.

• How many vehicles do we need assuming they serve differentregions differently?

atoriello@isye.gatech.edu

http://www.isye.gatech.edu/~atoriello3/